Path Planning And Error Analysis Of Large-diameter Optical Aspheric Grinding Processing

Large diameter optical systems are widely used in the observations of sky and earth.Since the aspherical mirror has good imaging quality,the large diameter optical system is composed of an aspheric mirror.For high precision,high efficiency,low-cost manufacturing aspheric mirrors,computer aided manufacturing techniques are developed,and ultra-fine grinding techniques have been used to replace the traditional grinding process.In this paper,based on the R2T2 configuration of a four-axis CNC composite grinding and polishing machine,the grinding geometry principle of large diameter optical aspheric surface of arc grinding wheel grinding processing is studied,the dynamic mathematical model of grinding wheel grinding edge in the workpiece coordinate system is established,and the motion trajectory equation between the grinding wheel and the workpiece cutting contact(that is,the grinding point)is given.Based on the differential geometric characteristics of the arc grinding wheel and the large diameter optical aspheric surface,the kinematic equations of the curved grinding wheel grinding processing optical aspheric surfaces of different machine tool configurations are established,and the kinematic equations based on the RT2 configuration machine tools are also established.According to the motion structu re of the four-axis CNC composite grinding and polishing machine tool,the motion model of the machine tool is established,and a special post-processing software is developed.According to the machine tool motion structure,a grinding simulation system is established based on VERICUT,and the simulation processing verification is carried out for the NC program generated by the post-processing.Combined with high-precision measurement technology,the surface contour after grinding and processing is measured in place,the data measurement path and error of the contact sensor are analyzed,and the error is corrected accordingly.The aspheric normal error function is established,and the coordinate points with large errors are obtained through programming calcu lations,and the NC program is modified according to the data of these points,and then the error compensation processing is performed on the aspheric surfaces.Qualitative analysis is given for the workpiece contour machining error generated by the fixed/ variable grinding point machining method,and the differential geometry principle is used to establish an approximate calculation error function for the contour error of the workpiece under these two machining methods and the wear of the arc grinding wheel,and the aspheric workpiece contour is predicted according to this error function.Finally,the high-order optical aspheric experiment of arc grinding wheel grinding processing was carried out,and the correctness of the post-processing algorithm was verified by motion simulation and experimental machining.At the same time,the four-axis fixed grinding point machining and the three-axis variable grinding point machining experiment were compared,which verified the relatively low motion error,"uniform" wear and relative durability of the variable grinding point machining.The correctness of the qualitative analysis of the contour error of the workpiece for fixed/variable grinding point machining and the correctness of the approximate calculation of the gri nding wheel wear function are verified.